Finite Group Databasebeta

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C₂×D₃×#23882 #72248169

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁶

Aliases

C₂×D₃×#23882

Splittings

Fitting	C₂×C₃×#23882 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#23882

Subgroups

	subgroup	G/H
center	C₂²	D₃×#2403
commutator, cosocle	C₂²×C₃×C₄	C₂⁶
Frattini	C₂²×C₄	C₂⁵×D₃
Fitting	C₂×C₃×#23882	C₂
socle	C₂²×C₃	C₂×#2403
hypercenter	C₂×#23882	D₃
hypocenter	C₃	C₂²×#23882
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#23882

Only the 5767 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72214076, D₃×#72215601, D₃×#72214565
maximal normal subgroup of	D₃×#72214076, D₃×#72215601, D₃×#72214565
maximal quotient of	D₃×#72214076
automorphism group of	C₂×#819

GAP

Past the SmallGroups library coverage — no SmallGroups id.